1 Data preparation

1.1 Outline

  • Load scripts: loads libraries and useful scripts used in the analyses; all .R files contained in scripts at the root of the factory are automatically loaded

  • Load data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.

1.2 Load packages


library(reportfactory)
library(here)
library(rio) 
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)

1.3 Load scripts

These scripts will load:

  • all scripts stored as .R files inside /scripts/
  • all scripts stored as .R files inside /src/

These scripts also contain routines to access the latest clean encrypted data (see next section).


reportfactory::rfh_load_scripts()

1.4 Load clean data

We import the latest NHS pathways data:


x <- import_pathways() %>%
  as_tibble()
x
## # A tibble: 155,735 x 11
##    site_type date       sex   age   ccg_code ccg_name count postcode nhs_region
##    <chr>     <date>     <chr> <chr> <chr>    <chr>    <int> <chr>    <chr>     
##  1 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    35 rm13ae   London    
##  2 111       2020-03-18 fema… 0-18  e380000… nhs_bed…    27 mk454hr  East of E…
##  3 111       2020-03-18 fema… 0-18  e380000… nhs_bla…     9 bb12fd   North West
##  4 111       2020-03-18 fema… 0-18  e380000… nhs_bro…    11 br33ql   London    
##  5 111       2020-03-18 fema… 0-18  e380000… nhs_can…     9 ws111jp  Midlands  
##  6 111       2020-03-18 fema… 0-18  e380000… nhs_cit…    12 n15lz    London    
##  7 111       2020-03-18 fema… 0-18  e380000… nhs_enf…     7 en40dy   London    
##  8 111       2020-03-18 fema… 0-18  e380000… nhs_ham…     6 dl62uu   North Eas…
##  9 111       2020-03-18 fema… 0-18  e380000… nhs_har…    24 ts232la  North Eas…
## 10 111       2020-03-18 fema… 0-18  e380000… nhs_kin…     6 kt11eu   London    
## # … with 155,725 more rows, and 2 more variables: day <int>, weekday <fct>

We also import demographics data for NHS regions in England, used later in our analysis:


path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
##                  nhs_region variable      value
## 1                North West     0-18 0.22538599
## 2  North East and Yorkshire     0-18 0.21876449
## 3                  Midlands     0-18 0.22564656
## 4           East of England     0-18 0.22810783
## 5                    London     0-18 0.23764782
## 6                South East     0-18 0.22458811
## 7                South West     0-18 0.20799797
## 8                North West    19-69 0.64274078
## 9  North East and Yorkshire    19-69 0.64437753
## 10                 Midlands    19-69 0.63876675
## 11          East of England    19-69 0.63034229
## 12                   London    19-69 0.67820084
## 13               South East    19-69 0.63267336
## 14               South West    19-69 0.63176131
## 15               North West   70-120 0.13187323
## 16 North East and Yorkshire   70-120 0.13685797
## 17                 Midlands   70-120 0.13558669
## 18          East of England   70-120 0.14154988
## 19                   London   70-120 0.08415135
## 20               South East   70-120 0.14273853
## 21               South West   70-120 0.16024072

Finally, we import publically available deaths per NHS region:


dth <- import_deaths() %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

#truncation to account for reporting delay
delay_max <- 21

dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
##     date_report               nhs_region deaths
## 1    2020-03-01          East of England      0
## 2    2020-03-02          East of England      1
## 3    2020-03-03          East of England      0
## 4    2020-03-04          East of England      0
## 5    2020-03-05          East of England      0
## 6    2020-03-06          East of England      1
## 7    2020-03-07          East of England      0
## 8    2020-03-08          East of England      0
## 9    2020-03-09          East of England      1
## 10   2020-03-10          East of England      0
## 11   2020-03-11          East of England      0
## 12   2020-03-12          East of England      0
## 13   2020-03-13          East of England      1
## 14   2020-03-14          East of England      2
## 15   2020-03-15          East of England      2
## 16   2020-03-16          East of England      1
## 17   2020-03-17          East of England      1
## 18   2020-03-18          East of England      5
## 19   2020-03-19          East of England      4
## 20   2020-03-20          East of England      2
## 21   2020-03-21          East of England     11
## 22   2020-03-22          East of England     12
## 23   2020-03-23          East of England     11
## 24   2020-03-24          East of England     19
## 25   2020-03-25          East of England     26
## 26   2020-03-26          East of England     36
## 27   2020-03-27          East of England     38
## 28   2020-03-28          East of England     28
## 29   2020-03-29          East of England     43
## 30   2020-03-30          East of England     45
## 31   2020-03-31          East of England     70
## 32   2020-04-01          East of England     62
## 33   2020-04-02          East of England     64
## 34   2020-04-03          East of England     80
## 35   2020-04-04          East of England     71
## 36   2020-04-05          East of England     76
## 37   2020-04-06          East of England     71
## 38   2020-04-07          East of England     93
## 39   2020-04-08          East of England    111
## 40   2020-04-09          East of England     87
## 41   2020-04-10          East of England     74
## 42   2020-04-11          East of England     92
## 43   2020-04-12          East of England    101
## 44   2020-04-13          East of England     78
## 45   2020-04-14          East of England     61
## 46   2020-04-15          East of England     82
## 47   2020-04-16          East of England     74
## 48   2020-04-17          East of England     86
## 49   2020-04-18          East of England     64
## 50   2020-04-19          East of England     67
## 51   2020-04-20          East of England     67
## 52   2020-04-21          East of England     75
## 53   2020-04-22          East of England     67
## 54   2020-04-23          East of England     49
## 55   2020-04-24          East of England     66
## 56   2020-04-25          East of England     54
## 57   2020-04-26          East of England     48
## 58   2020-04-27          East of England     46
## 59   2020-04-28          East of England     58
## 60   2020-04-29          East of England     32
## 61   2020-04-30          East of England     45
## 62   2020-05-01          East of England     49
## 63   2020-05-02          East of England     29
## 64   2020-05-03          East of England     41
## 65   2020-05-04          East of England     19
## 66   2020-05-05          East of England     36
## 67   2020-05-06          East of England     31
## 68   2020-05-07          East of England     33
## 69   2020-05-08          East of England     33
## 70   2020-05-09          East of England     29
## 71   2020-05-10          East of England     22
## 72   2020-05-11          East of England     18
## 73   2020-05-12          East of England     21
## 74   2020-05-13          East of England     27
## 75   2020-05-14          East of England     26
## 76   2020-05-15          East of England     19
## 77   2020-05-16          East of England     26
## 78   2020-05-17          East of England     17
## 79   2020-05-18          East of England     25
## 80   2020-05-19          East of England     15
## 81   2020-05-20          East of England     26
## 82   2020-05-21          East of England     21
## 83   2020-05-22          East of England     13
## 84   2020-05-23          East of England     12
## 85   2020-05-24          East of England     17
## 86   2020-05-25          East of England     25
## 87   2020-05-26          East of England     14
## 88   2020-05-27          East of England     12
## 89   2020-05-28          East of England     17
## 90   2020-05-29          East of England     16
## 91   2020-05-30          East of England      9
## 92   2020-05-31          East of England      8
## 93   2020-06-01          East of England     17
## 94   2020-06-02          East of England     14
## 95   2020-06-03          East of England     10
## 96   2020-06-04          East of England      7
## 97   2020-06-05          East of England     12
## 98   2020-06-06          East of England      5
## 99   2020-06-07          East of England      9
## 100  2020-06-08          East of England      5
## 101  2020-06-09          East of England      6
## 102  2020-06-10          East of England      8
## 103  2020-06-11          East of England      0
## 104  2020-06-12          East of England      9
## 105  2020-06-13          East of England      5
## 106  2020-06-14          East of England      4
## 107  2020-06-15          East of England      7
## 108  2020-06-16          East of England      3
## 109  2020-06-17          East of England      7
## 110  2020-06-18          East of England      4
## 111  2020-06-19          East of England      6
## 112  2020-06-20          East of England      2
## 113  2020-06-21          East of England      2
## 114  2020-06-22          East of England      1
## 115  2020-03-01                   London      0
## 116  2020-03-02                   London      0
## 117  2020-03-03                   London      0
## 118  2020-03-04                   London      0
## 119  2020-03-05                   London      0
## 120  2020-03-06                   London      1
## 121  2020-03-07                   London      0
## 122  2020-03-08                   London      0
## 123  2020-03-09                   London      1
## 124  2020-03-10                   London      0
## 125  2020-03-11                   London      6
## 126  2020-03-12                   London      6
## 127  2020-03-13                   London     10
## 128  2020-03-14                   London     14
## 129  2020-03-15                   London     10
## 130  2020-03-16                   London     15
## 131  2020-03-17                   London     23
## 132  2020-03-18                   London     27
## 133  2020-03-19                   London     25
## 134  2020-03-20                   London     44
## 135  2020-03-21                   London     49
## 136  2020-03-22                   London     54
## 137  2020-03-23                   London     63
## 138  2020-03-24                   London     87
## 139  2020-03-25                   London    113
## 140  2020-03-26                   London    129
## 141  2020-03-27                   London    130
## 142  2020-03-28                   London    122
## 143  2020-03-29                   London    146
## 144  2020-03-30                   London    149
## 145  2020-03-31                   London    181
## 146  2020-04-01                   London    202
## 147  2020-04-02                   London    190
## 148  2020-04-03                   London    196
## 149  2020-04-04                   London    230
## 150  2020-04-05                   London    195
## 151  2020-04-06                   London    197
## 152  2020-04-07                   London    220
## 153  2020-04-08                   London    238
## 154  2020-04-09                   London    206
## 155  2020-04-10                   London    170
## 156  2020-04-11                   London    178
## 157  2020-04-12                   London    158
## 158  2020-04-13                   London    166
## 159  2020-04-14                   London    144
## 160  2020-04-15                   London    142
## 161  2020-04-16                   London    139
## 162  2020-04-17                   London    100
## 163  2020-04-18                   London    101
## 164  2020-04-19                   London    103
## 165  2020-04-20                   London     95
## 166  2020-04-21                   London     94
## 167  2020-04-22                   London    109
## 168  2020-04-23                   London     77
## 169  2020-04-24                   London     71
## 170  2020-04-25                   London     58
## 171  2020-04-26                   London     53
## 172  2020-04-27                   London     51
## 173  2020-04-28                   London     43
## 174  2020-04-29                   London     44
## 175  2020-04-30                   London     40
## 176  2020-05-01                   London     41
## 177  2020-05-02                   London     41
## 178  2020-05-03                   London     36
## 179  2020-05-04                   London     30
## 180  2020-05-05                   London     25
## 181  2020-05-06                   London     37
## 182  2020-05-07                   London     37
## 183  2020-05-08                   London     30
## 184  2020-05-09                   London     23
## 185  2020-05-10                   London     26
## 186  2020-05-11                   London     18
## 187  2020-05-12                   London     18
## 188  2020-05-13                   London     16
## 189  2020-05-14                   London     20
## 190  2020-05-15                   London     18
## 191  2020-05-16                   London     14
## 192  2020-05-17                   London     15
## 193  2020-05-18                   London      9
## 194  2020-05-19                   London     14
## 195  2020-05-20                   London     19
## 196  2020-05-21                   London     12
## 197  2020-05-22                   London     10
## 198  2020-05-23                   London      6
## 199  2020-05-24                   London      7
## 200  2020-05-25                   London      9
## 201  2020-05-26                   London     12
## 202  2020-05-27                   London      7
## 203  2020-05-28                   London      8
## 204  2020-05-29                   London      7
## 205  2020-05-30                   London     12
## 206  2020-05-31                   London      6
## 207  2020-06-01                   London     10
## 208  2020-06-02                   London      7
## 209  2020-06-03                   London      6
## 210  2020-06-04                   London      8
## 211  2020-06-05                   London      4
## 212  2020-06-06                   London      0
## 213  2020-06-07                   London      4
## 214  2020-06-08                   London      5
## 215  2020-06-09                   London      4
## 216  2020-06-10                   London      7
## 217  2020-06-11                   London      5
## 218  2020-06-12                   London      3
## 219  2020-06-13                   London      3
## 220  2020-06-14                   London      2
## 221  2020-06-15                   London      1
## 222  2020-06-16                   London      2
## 223  2020-06-17                   London      1
## 224  2020-06-18                   London      2
## 225  2020-06-19                   London      1
## 226  2020-06-20                   London      1
## 227  2020-06-21                   London      1
## 228  2020-06-22                   London      0
## 229  2020-03-01                 Midlands      0
## 230  2020-03-02                 Midlands      0
## 231  2020-03-03                 Midlands      1
## 232  2020-03-04                 Midlands      0
## 233  2020-03-05                 Midlands      0
## 234  2020-03-06                 Midlands      0
## 235  2020-03-07                 Midlands      0
## 236  2020-03-08                 Midlands      3
## 237  2020-03-09                 Midlands      1
## 238  2020-03-10                 Midlands      0
## 239  2020-03-11                 Midlands      2
## 240  2020-03-12                 Midlands      6
## 241  2020-03-13                 Midlands      5
## 242  2020-03-14                 Midlands      4
## 243  2020-03-15                 Midlands      5
## 244  2020-03-16                 Midlands     11
## 245  2020-03-17                 Midlands      8
## 246  2020-03-18                 Midlands     13
## 247  2020-03-19                 Midlands      8
## 248  2020-03-20                 Midlands     28
## 249  2020-03-21                 Midlands     13
## 250  2020-03-22                 Midlands     31
## 251  2020-03-23                 Midlands     33
## 252  2020-03-24                 Midlands     41
## 253  2020-03-25                 Midlands     48
## 254  2020-03-26                 Midlands     64
## 255  2020-03-27                 Midlands     72
## 256  2020-03-28                 Midlands     89
## 257  2020-03-29                 Midlands     92
## 258  2020-03-30                 Midlands     90
## 259  2020-03-31                 Midlands    123
## 260  2020-04-01                 Midlands    140
## 261  2020-04-02                 Midlands    142
## 262  2020-04-03                 Midlands    124
## 263  2020-04-04                 Midlands    151
## 264  2020-04-05                 Midlands    164
## 265  2020-04-06                 Midlands    140
## 266  2020-04-07                 Midlands    123
## 267  2020-04-08                 Midlands    186
## 268  2020-04-09                 Midlands    139
## 269  2020-04-10                 Midlands    127
## 270  2020-04-11                 Midlands    142
## 271  2020-04-12                 Midlands    139
## 272  2020-04-13                 Midlands    120
## 273  2020-04-14                 Midlands    116
## 274  2020-04-15                 Midlands    147
## 275  2020-04-16                 Midlands    102
## 276  2020-04-17                 Midlands    118
## 277  2020-04-18                 Midlands    115
## 278  2020-04-19                 Midlands     92
## 279  2020-04-20                 Midlands    107
## 280  2020-04-21                 Midlands     86
## 281  2020-04-22                 Midlands     78
## 282  2020-04-23                 Midlands    103
## 283  2020-04-24                 Midlands     79
## 284  2020-04-25                 Midlands     72
## 285  2020-04-26                 Midlands     81
## 286  2020-04-27                 Midlands     74
## 287  2020-04-28                 Midlands     68
## 288  2020-04-29                 Midlands     53
## 289  2020-04-30                 Midlands     56
## 290  2020-05-01                 Midlands     64
## 291  2020-05-02                 Midlands     51
## 292  2020-05-03                 Midlands     52
## 293  2020-05-04                 Midlands     61
## 294  2020-05-05                 Midlands     58
## 295  2020-05-06                 Midlands     59
## 296  2020-05-07                 Midlands     48
## 297  2020-05-08                 Midlands     34
## 298  2020-05-09                 Midlands     37
## 299  2020-05-10                 Midlands     42
## 300  2020-05-11                 Midlands     33
## 301  2020-05-12                 Midlands     45
## 302  2020-05-13                 Midlands     40
## 303  2020-05-14                 Midlands     37
## 304  2020-05-15                 Midlands     40
## 305  2020-05-16                 Midlands     34
## 306  2020-05-17                 Midlands     31
## 307  2020-05-18                 Midlands     34
## 308  2020-05-19                 Midlands     34
## 309  2020-05-20                 Midlands     36
## 310  2020-05-21                 Midlands     32
## 311  2020-05-22                 Midlands     27
## 312  2020-05-23                 Midlands     34
## 313  2020-05-24                 Midlands     19
## 314  2020-05-25                 Midlands     26
## 315  2020-05-26                 Midlands     33
## 316  2020-05-27                 Midlands     29
## 317  2020-05-28                 Midlands     27
## 318  2020-05-29                 Midlands     20
## 319  2020-05-30                 Midlands     20
## 320  2020-05-31                 Midlands     22
## 321  2020-06-01                 Midlands     20
## 322  2020-06-02                 Midlands     22
## 323  2020-06-03                 Midlands     24
## 324  2020-06-04                 Midlands     15
## 325  2020-06-05                 Midlands     21
## 326  2020-06-06                 Midlands     20
## 327  2020-06-07                 Midlands     16
## 328  2020-06-08                 Midlands     15
## 329  2020-06-09                 Midlands     17
## 330  2020-06-10                 Midlands     15
## 331  2020-06-11                 Midlands     13
## 332  2020-06-12                 Midlands     12
## 333  2020-06-13                 Midlands      6
## 334  2020-06-14                 Midlands     17
## 335  2020-06-15                 Midlands     12
## 336  2020-06-16                 Midlands     14
## 337  2020-06-17                 Midlands     10
## 338  2020-06-18                 Midlands     14
## 339  2020-06-19                 Midlands      7
## 340  2020-06-20                 Midlands      9
## 341  2020-06-21                 Midlands      6
## 342  2020-06-22                 Midlands      0
## 343  2020-03-01 North East and Yorkshire      0
## 344  2020-03-02 North East and Yorkshire      0
## 345  2020-03-03 North East and Yorkshire      0
## 346  2020-03-04 North East and Yorkshire      0
## 347  2020-03-05 North East and Yorkshire      0
## 348  2020-03-06 North East and Yorkshire      0
## 349  2020-03-07 North East and Yorkshire      0
## 350  2020-03-08 North East and Yorkshire      0
## 351  2020-03-09 North East and Yorkshire      0
## 352  2020-03-10 North East and Yorkshire      0
## 353  2020-03-11 North East and Yorkshire      0
## 354  2020-03-12 North East and Yorkshire      0
## 355  2020-03-13 North East and Yorkshire      0
## 356  2020-03-14 North East and Yorkshire      0
## 357  2020-03-15 North East and Yorkshire      2
## 358  2020-03-16 North East and Yorkshire      3
## 359  2020-03-17 North East and Yorkshire      1
## 360  2020-03-18 North East and Yorkshire      2
## 361  2020-03-19 North East and Yorkshire      6
## 362  2020-03-20 North East and Yorkshire      5
## 363  2020-03-21 North East and Yorkshire      6
## 364  2020-03-22 North East and Yorkshire      7
## 365  2020-03-23 North East and Yorkshire      9
## 366  2020-03-24 North East and Yorkshire      8
## 367  2020-03-25 North East and Yorkshire     18
## 368  2020-03-26 North East and Yorkshire     21
## 369  2020-03-27 North East and Yorkshire     28
## 370  2020-03-28 North East and Yorkshire     35
## 371  2020-03-29 North East and Yorkshire     38
## 372  2020-03-30 North East and Yorkshire     64
## 373  2020-03-31 North East and Yorkshire     60
## 374  2020-04-01 North East and Yorkshire     67
## 375  2020-04-02 North East and Yorkshire     74
## 376  2020-04-03 North East and Yorkshire    100
## 377  2020-04-04 North East and Yorkshire    105
## 378  2020-04-05 North East and Yorkshire     92
## 379  2020-04-06 North East and Yorkshire     96
## 380  2020-04-07 North East and Yorkshire    102
## 381  2020-04-08 North East and Yorkshire    107
## 382  2020-04-09 North East and Yorkshire    111
## 383  2020-04-10 North East and Yorkshire    117
## 384  2020-04-11 North East and Yorkshire     98
## 385  2020-04-12 North East and Yorkshire     84
## 386  2020-04-13 North East and Yorkshire     94
## 387  2020-04-14 North East and Yorkshire    107
## 388  2020-04-15 North East and Yorkshire     96
## 389  2020-04-16 North East and Yorkshire    103
## 390  2020-04-17 North East and Yorkshire     88
## 391  2020-04-18 North East and Yorkshire     95
## 392  2020-04-19 North East and Yorkshire     88
## 393  2020-04-20 North East and Yorkshire    100
## 394  2020-04-21 North East and Yorkshire     76
## 395  2020-04-22 North East and Yorkshire     84
## 396  2020-04-23 North East and Yorkshire     63
## 397  2020-04-24 North East and Yorkshire     72
## 398  2020-04-25 North East and Yorkshire     69
## 399  2020-04-26 North East and Yorkshire     65
## 400  2020-04-27 North East and Yorkshire     65
## 401  2020-04-28 North East and Yorkshire     57
## 402  2020-04-29 North East and Yorkshire     69
## 403  2020-04-30 North East and Yorkshire     57
## 404  2020-05-01 North East and Yorkshire     64
## 405  2020-05-02 North East and Yorkshire     48
## 406  2020-05-03 North East and Yorkshire     40
## 407  2020-05-04 North East and Yorkshire     49
## 408  2020-05-05 North East and Yorkshire     40
## 409  2020-05-06 North East and Yorkshire     51
## 410  2020-05-07 North East and Yorkshire     45
## 411  2020-05-08 North East and Yorkshire     42
## 412  2020-05-09 North East and Yorkshire     44
## 413  2020-05-10 North East and Yorkshire     40
## 414  2020-05-11 North East and Yorkshire     29
## 415  2020-05-12 North East and Yorkshire     27
## 416  2020-05-13 North East and Yorkshire     28
## 417  2020-05-14 North East and Yorkshire     31
## 418  2020-05-15 North East and Yorkshire     32
## 419  2020-05-16 North East and Yorkshire     35
## 420  2020-05-17 North East and Yorkshire     26
## 421  2020-05-18 North East and Yorkshire     30
## 422  2020-05-19 North East and Yorkshire     27
## 423  2020-05-20 North East and Yorkshire     22
## 424  2020-05-21 North East and Yorkshire     33
## 425  2020-05-22 North East and Yorkshire     22
## 426  2020-05-23 North East and Yorkshire     18
## 427  2020-05-24 North East and Yorkshire     26
## 428  2020-05-25 North East and Yorkshire     21
## 429  2020-05-26 North East and Yorkshire     21
## 430  2020-05-27 North East and Yorkshire     22
## 431  2020-05-28 North East and Yorkshire     20
## 432  2020-05-29 North East and Yorkshire     25
## 433  2020-05-30 North East and Yorkshire     20
## 434  2020-05-31 North East and Yorkshire     20
## 435  2020-06-01 North East and Yorkshire     16
## 436  2020-06-02 North East and Yorkshire     23
## 437  2020-06-03 North East and Yorkshire     22
## 438  2020-06-04 North East and Yorkshire     17
## 439  2020-06-05 North East and Yorkshire     17
## 440  2020-06-06 North East and Yorkshire     21
## 441  2020-06-07 North East and Yorkshire     13
## 442  2020-06-08 North East and Yorkshire     11
## 443  2020-06-09 North East and Yorkshire     11
## 444  2020-06-10 North East and Yorkshire     18
## 445  2020-06-11 North East and Yorkshire      7
## 446  2020-06-12 North East and Yorkshire      9
## 447  2020-06-13 North East and Yorkshire     10
## 448  2020-06-14 North East and Yorkshire     11
## 449  2020-06-15 North East and Yorkshire      8
## 450  2020-06-16 North East and Yorkshire     10
## 451  2020-06-17 North East and Yorkshire      7
## 452  2020-06-18 North East and Yorkshire      7
## 453  2020-06-19 North East and Yorkshire      4
## 454  2020-06-20 North East and Yorkshire      4
## 455  2020-06-21 North East and Yorkshire      3
## 456  2020-06-22 North East and Yorkshire      3
## 457  2020-03-01               North West      0
## 458  2020-03-02               North West      0
## 459  2020-03-03               North West      0
## 460  2020-03-04               North West      0
## 461  2020-03-05               North West      1
## 462  2020-03-06               North West      0
## 463  2020-03-07               North West      0
## 464  2020-03-08               North West      1
## 465  2020-03-09               North West      0
## 466  2020-03-10               North West      0
## 467  2020-03-11               North West      0
## 468  2020-03-12               North West      2
## 469  2020-03-13               North West      3
## 470  2020-03-14               North West      1
## 471  2020-03-15               North West      4
## 472  2020-03-16               North West      2
## 473  2020-03-17               North West      4
## 474  2020-03-18               North West      6
## 475  2020-03-19               North West      7
## 476  2020-03-20               North West     10
## 477  2020-03-21               North West     11
## 478  2020-03-22               North West     13
## 479  2020-03-23               North West     15
## 480  2020-03-24               North West     21
## 481  2020-03-25               North West     21
## 482  2020-03-26               North West     29
## 483  2020-03-27               North West     35
## 484  2020-03-28               North West     28
## 485  2020-03-29               North West     46
## 486  2020-03-30               North West     67
## 487  2020-03-31               North West     52
## 488  2020-04-01               North West     86
## 489  2020-04-02               North West     96
## 490  2020-04-03               North West     95
## 491  2020-04-04               North West     98
## 492  2020-04-05               North West    102
## 493  2020-04-06               North West    100
## 494  2020-04-07               North West    135
## 495  2020-04-08               North West    127
## 496  2020-04-09               North West    119
## 497  2020-04-10               North West    117
## 498  2020-04-11               North West    138
## 499  2020-04-12               North West    125
## 500  2020-04-13               North West    129
## 501  2020-04-14               North West    131
## 502  2020-04-15               North West    114
## 503  2020-04-16               North West    135
## 504  2020-04-17               North West     98
## 505  2020-04-18               North West    113
## 506  2020-04-19               North West     71
## 507  2020-04-20               North West     83
## 508  2020-04-21               North West     76
## 509  2020-04-22               North West     86
## 510  2020-04-23               North West     85
## 511  2020-04-24               North West     66
## 512  2020-04-25               North West     65
## 513  2020-04-26               North West     55
## 514  2020-04-27               North West     54
## 515  2020-04-28               North West     57
## 516  2020-04-29               North West     62
## 517  2020-04-30               North West     59
## 518  2020-05-01               North West     45
## 519  2020-05-02               North West     56
## 520  2020-05-03               North West     55
## 521  2020-05-04               North West     48
## 522  2020-05-05               North West     48
## 523  2020-05-06               North West     44
## 524  2020-05-07               North West     49
## 525  2020-05-08               North West     42
## 526  2020-05-09               North West     30
## 527  2020-05-10               North West     41
## 528  2020-05-11               North West     35
## 529  2020-05-12               North West     38
## 530  2020-05-13               North West     25
## 531  2020-05-14               North West     26
## 532  2020-05-15               North West     33
## 533  2020-05-16               North West     32
## 534  2020-05-17               North West     24
## 535  2020-05-18               North West     31
## 536  2020-05-19               North West     35
## 537  2020-05-20               North West     27
## 538  2020-05-21               North West     26
## 539  2020-05-22               North West     26
## 540  2020-05-23               North West     31
## 541  2020-05-24               North West     26
## 542  2020-05-25               North West     31
## 543  2020-05-26               North West     27
## 544  2020-05-27               North West     27
## 545  2020-05-28               North West     28
## 546  2020-05-29               North West     20
## 547  2020-05-30               North West     19
## 548  2020-05-31               North West     13
## 549  2020-06-01               North West     12
## 550  2020-06-02               North West     27
## 551  2020-06-03               North West     22
## 552  2020-06-04               North West     22
## 553  2020-06-05               North West     15
## 554  2020-06-06               North West     23
## 555  2020-06-07               North West     19
## 556  2020-06-08               North West     20
## 557  2020-06-09               North West     15
## 558  2020-06-10               North West     14
## 559  2020-06-11               North West     16
## 560  2020-06-12               North West      7
## 561  2020-06-13               North West      8
## 562  2020-06-14               North West     15
## 563  2020-06-15               North West     15
## 564  2020-06-16               North West     11
## 565  2020-06-17               North West     10
## 566  2020-06-18               North West      9
## 567  2020-06-19               North West      7
## 568  2020-06-20               North West      8
## 569  2020-06-21               North West      4
## 570  2020-06-22               North West      2
## 571  2020-03-01               South East      0
## 572  2020-03-02               South East      0
## 573  2020-03-03               South East      1
## 574  2020-03-04               South East      0
## 575  2020-03-05               South East      1
## 576  2020-03-06               South East      0
## 577  2020-03-07               South East      0
## 578  2020-03-08               South East      1
## 579  2020-03-09               South East      1
## 580  2020-03-10               South East      1
## 581  2020-03-11               South East      1
## 582  2020-03-12               South East      0
## 583  2020-03-13               South East      1
## 584  2020-03-14               South East      1
## 585  2020-03-15               South East      5
## 586  2020-03-16               South East      8
## 587  2020-03-17               South East      7
## 588  2020-03-18               South East     10
## 589  2020-03-19               South East      9
## 590  2020-03-20               South East     13
## 591  2020-03-21               South East      7
## 592  2020-03-22               South East     25
## 593  2020-03-23               South East     20
## 594  2020-03-24               South East     22
## 595  2020-03-25               South East     29
## 596  2020-03-26               South East     35
## 597  2020-03-27               South East     34
## 598  2020-03-28               South East     36
## 599  2020-03-29               South East     55
## 600  2020-03-30               South East     58
## 601  2020-03-31               South East     65
## 602  2020-04-01               South East     66
## 603  2020-04-02               South East     55
## 604  2020-04-03               South East     72
## 605  2020-04-04               South East     80
## 606  2020-04-05               South East     82
## 607  2020-04-06               South East     88
## 608  2020-04-07               South East    100
## 609  2020-04-08               South East     83
## 610  2020-04-09               South East    104
## 611  2020-04-10               South East     88
## 612  2020-04-11               South East     88
## 613  2020-04-12               South East     88
## 614  2020-04-13               South East     84
## 615  2020-04-14               South East     65
## 616  2020-04-15               South East     72
## 617  2020-04-16               South East     56
## 618  2020-04-17               South East     86
## 619  2020-04-18               South East     57
## 620  2020-04-19               South East     70
## 621  2020-04-20               South East     87
## 622  2020-04-21               South East     50
## 623  2020-04-22               South East     54
## 624  2020-04-23               South East     57
## 625  2020-04-24               South East     64
## 626  2020-04-25               South East     51
## 627  2020-04-26               South East     51
## 628  2020-04-27               South East     40
## 629  2020-04-28               South East     40
## 630  2020-04-29               South East     47
## 631  2020-04-30               South East     29
## 632  2020-05-01               South East     37
## 633  2020-05-02               South East     36
## 634  2020-05-03               South East     17
## 635  2020-05-04               South East     35
## 636  2020-05-05               South East     29
## 637  2020-05-06               South East     25
## 638  2020-05-07               South East     27
## 639  2020-05-08               South East     26
## 640  2020-05-09               South East     28
## 641  2020-05-10               South East     19
## 642  2020-05-11               South East     25
## 643  2020-05-12               South East     27
## 644  2020-05-13               South East     18
## 645  2020-05-14               South East     32
## 646  2020-05-15               South East     24
## 647  2020-05-16               South East     22
## 648  2020-05-17               South East     18
## 649  2020-05-18               South East     22
## 650  2020-05-19               South East     12
## 651  2020-05-20               South East     22
## 652  2020-05-21               South East     15
## 653  2020-05-22               South East     17
## 654  2020-05-23               South East     21
## 655  2020-05-24               South East     17
## 656  2020-05-25               South East     13
## 657  2020-05-26               South East     19
## 658  2020-05-27               South East     18
## 659  2020-05-28               South East     12
## 660  2020-05-29               South East     21
## 661  2020-05-30               South East      8
## 662  2020-05-31               South East     10
## 663  2020-06-01               South East     11
## 664  2020-06-02               South East     13
## 665  2020-06-03               South East     17
## 666  2020-06-04               South East     11
## 667  2020-06-05               South East     11
## 668  2020-06-06               South East     10
## 669  2020-06-07               South East     11
## 670  2020-06-08               South East      7
## 671  2020-06-09               South East     10
## 672  2020-06-10               South East     10
## 673  2020-06-11               South East      5
## 674  2020-06-12               South East      5
## 675  2020-06-13               South East      4
## 676  2020-06-14               South East      6
## 677  2020-06-15               South East      7
## 678  2020-06-16               South East     10
## 679  2020-06-17               South East      8
## 680  2020-06-18               South East      4
## 681  2020-06-19               South East      5
## 682  2020-06-20               South East      4
## 683  2020-06-21               South East      1
## 684  2020-06-22               South East      0
## 685  2020-03-01               South West      0
## 686  2020-03-02               South West      0
## 687  2020-03-03               South West      0
## 688  2020-03-04               South West      0
## 689  2020-03-05               South West      0
## 690  2020-03-06               South West      0
## 691  2020-03-07               South West      0
## 692  2020-03-08               South West      0
## 693  2020-03-09               South West      0
## 694  2020-03-10               South West      0
## 695  2020-03-11               South West      1
## 696  2020-03-12               South West      0
## 697  2020-03-13               South West      0
## 698  2020-03-14               South West      1
## 699  2020-03-15               South West      0
## 700  2020-03-16               South West      0
## 701  2020-03-17               South West      2
## 702  2020-03-18               South West      2
## 703  2020-03-19               South West      4
## 704  2020-03-20               South West      3
## 705  2020-03-21               South West      6
## 706  2020-03-22               South West      7
## 707  2020-03-23               South West      8
## 708  2020-03-24               South West      7
## 709  2020-03-25               South West      9
## 710  2020-03-26               South West     11
## 711  2020-03-27               South West     13
## 712  2020-03-28               South West     21
## 713  2020-03-29               South West     18
## 714  2020-03-30               South West     23
## 715  2020-03-31               South West     23
## 716  2020-04-01               South West     22
## 717  2020-04-02               South West     23
## 718  2020-04-03               South West     30
## 719  2020-04-04               South West     42
## 720  2020-04-05               South West     32
## 721  2020-04-06               South West     34
## 722  2020-04-07               South West     39
## 723  2020-04-08               South West     47
## 724  2020-04-09               South West     24
## 725  2020-04-10               South West     46
## 726  2020-04-11               South West     43
## 727  2020-04-12               South West     23
## 728  2020-04-13               South West     27
## 729  2020-04-14               South West     24
## 730  2020-04-15               South West     32
## 731  2020-04-16               South West     29
## 732  2020-04-17               South West     33
## 733  2020-04-18               South West     25
## 734  2020-04-19               South West     31
## 735  2020-04-20               South West     26
## 736  2020-04-21               South West     26
## 737  2020-04-22               South West     23
## 738  2020-04-23               South West     17
## 739  2020-04-24               South West     19
## 740  2020-04-25               South West     15
## 741  2020-04-26               South West     27
## 742  2020-04-27               South West     13
## 743  2020-04-28               South West     17
## 744  2020-04-29               South West     15
## 745  2020-04-30               South West     26
## 746  2020-05-01               South West      6
## 747  2020-05-02               South West      7
## 748  2020-05-03               South West     10
## 749  2020-05-04               South West     17
## 750  2020-05-05               South West     14
## 751  2020-05-06               South West     19
## 752  2020-05-07               South West     16
## 753  2020-05-08               South West      6
## 754  2020-05-09               South West     11
## 755  2020-05-10               South West      5
## 756  2020-05-11               South West      8
## 757  2020-05-12               South West      7
## 758  2020-05-13               South West      7
## 759  2020-05-14               South West      6
## 760  2020-05-15               South West      4
## 761  2020-05-16               South West      4
## 762  2020-05-17               South West      6
## 763  2020-05-18               South West      4
## 764  2020-05-19               South West      6
## 765  2020-05-20               South West      1
## 766  2020-05-21               South West      9
## 767  2020-05-22               South West      6
## 768  2020-05-23               South West      6
## 769  2020-05-24               South West      3
## 770  2020-05-25               South West      8
## 771  2020-05-26               South West     11
## 772  2020-05-27               South West      5
## 773  2020-05-28               South West     10
## 774  2020-05-29               South West      7
## 775  2020-05-30               South West      3
## 776  2020-05-31               South West      2
## 777  2020-06-01               South West      7
## 778  2020-06-02               South West      2
## 779  2020-06-03               South West      5
## 780  2020-06-04               South West      2
## 781  2020-06-05               South West      2
## 782  2020-06-06               South West      1
## 783  2020-06-07               South West      3
## 784  2020-06-08               South West      3
## 785  2020-06-09               South West      0
## 786  2020-06-10               South West      0
## 787  2020-06-11               South West      2
## 788  2020-06-12               South West      2
## 789  2020-06-13               South West      2
## 790  2020-06-14               South West      0
## 791  2020-06-15               South West      1
## 792  2020-06-16               South West      1
## 793  2020-06-17               South West      0
## 794  2020-06-18               South West      0
## 795  2020-06-19               South West      0
## 796  2020-06-20               South West      2
## 797  2020-06-21               South West      0
## 798  2020-06-22               South West      0

1.5 Completion date

We extract the completion date from the NHS Pathways file timestamp:


database_date <- attr(x, "timestamp")
database_date
## [1] "2020-06-23"

The completion date of the NHS Pathways data is Tuesday 23 Jun 2020.

1.6 Auxiliary functions

These are functions which will be used further in the analyses.

Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:


## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here

Rsq <- function(x) {
  1 - (x$deviance / x$null.deviance)
}

Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:


## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals

get_r <- function(model) {
  ##  extract coefficients and conf int
  out <- data.frame(r = coef(model))  %>%
    rownames_to_column("var") %>% 
    cbind(confint(model)) %>%
    filter(!grepl("day_of_week", var)) %>% 
    filter(grepl("day", var)) %>%
    rename(lower_95 = "2.5 %",
           upper_95 = "97.5 %") %>%
    mutate(var = sub("day:", "", var))
  
  ## reconstruct values: intercept + region-coefficient
  for (i in 2:nrow(out)) {
    out[i, -1] <- out[1, -1] + out[i, -1]
  }
  
  ## find the name of the intercept, restore regions names
  out <- out %>%
    mutate(nhs_region = model$xlevels$nhs_region) %>%
    select(nhs_region, everything(), -var)
  
  ## find halving times
  halving <- log(0.5) / out[,-1] %>%
    rename(halving_t = r,
           halving_t_lower_95 = lower_95,
           halving_t_upper_95 = upper_95)
  
  ## set halving times with exclusion intervals to NA
  no_halving <- out$lower_95 < 0 & out$upper_95 > 0
  halving[no_halving, ] <- NA_real_
  
  ## return all data
  cbind(out, halving)
  
}

Functions used in the correlation analysis between NHS Pathways reports and deaths:

## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.

getcor <- function(x, ndx) {
  return(cor(x$deaths[ndx],
             x$note_lag[ndx],
             use = "complete.obs",
             method = "pearson"))
}

## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)

getboot <- function(x) {
  result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000), 
                           type = "bca")
  return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
                    r = result$t0,
                    r_low = result$bca[4],
                    r_hi = result$bca[5]))
}

Function to classify the day of the week into weekend, Monday, and the rest:


## Fn to add day of week
day_of_week <- function(df) {
  df %>% 
    dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>% 
    dplyr::mutate(day_of_week = dplyr::case_when(
      day_of_week %in% c("Sat", "Sun") ~ "weekend",
      day_of_week %in% c("Mon") ~ "monday",
      !(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
    ) %>% 
      factor(levels = c("rest_of_week", "monday", "weekend")))
}

Custom color palettes, color scales, and vectors of colors:


pal <- c("#006212",
         "#ae3cab",
         "#00db90",
         "#960c00",
         "#55aaff",
         "#ff7e78",
         "#00388d")

age.pal <- viridis::viridis(3,begin = 0.1, end = 0.7)

3 Comparison with deaths time series

3.1 Outline

We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.

Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.

3.2 Lagged correlation

We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.

First we join the NHS Pathways and death data, and aggregate over all England:

## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max

dth_trunc <- dth %>%
  rename(date = date_report) %>%
  filter(date <= trunc_date) 

## join with notification data
all_data <- x %>% 
  filter(!is.na(nhs_region)) %>%
  group_by(date, nhs_region) %>%
  summarise(count = sum(count, na.rm = T)) %>%
  ungroup %>%
  inner_join(dth_trunc,
             by = c("date","nhs_region"))

all_tot <- all_data %>%
  group_by(date) %>%
  summarise(count = sum(count, na.rm = TRUE),
            deaths = sum(deaths, na.rm = TRUE)) 

We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:


## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
  
  ## lag reports
  summary <- all_tot %>% 
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI
    getboot(.) %>%
    mutate(lag = i)

  lag_cor <- bind_rows(lag_cor, summary)
}

cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
  theme_bw() +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_point() +
  geom_line() +
  labs(x = "Lag between NHS pathways and death data (days)",
       y = "Pearson's correlation") +
  large_txt
cor_vs_lag


l_opt <- which.max(lag_cor$r)

This analysis suggests that the best lag is 23 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 23 days.


all_tot <- all_tot %>%
  rename(date_death = date) %>%
  mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
         note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
         date_note = lag(date_death,16))

lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")

summary(lag_mod)
## 
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -9.9764  -2.5429  -0.3049   3.3258   5.4572  
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 4.897e+00  5.397e-02   90.73   <2e-16 ***
## note_lag    1.205e-05  5.447e-07   22.12   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 12.50936)
## 
##     Null deviance: 6551.43  on 52  degrees of freedom
## Residual deviance:  660.19  on 51  degrees of freedom
##   (23 observations deleted due to missingness)
## AIC: NA
## 
## Number of Fisher Scoring iterations: 4

exp(coefficients(lag_mod))
## (Intercept)    note_lag 
##  133.826168    1.000012
exp(confint(lag_mod))
##                  2.5 %     97.5 %
## (Intercept) 120.244966 148.579316
## note_lag      1.000011   1.000013

Rsq(lag_mod)
## [1] 0.8992302

mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])

all_tot_pred <- 
  all_tot %>%
  filter(!is.na(note_lag)) %>%
  mutate(pred = mod_fit$fit,
         pred.se = mod_fit$se.fit,
         low = exp(pred - 1.96*pred.se),
         hi = exp(pred + 1.96*pred.se))


glm_fit <- all_tot_pred %>% 
    filter(!is.na(note_lag)) %>%
  ggplot(aes(x = note_lag, y = deaths)) +
  geom_point() + 
  geom_line(aes(y = exp(pred))) + 
  geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
  theme_bw() +
  labs(y = "Daily number of\ndeaths reported",
       x = "Daily number of NHS Pathways reports") +
  large_txt

glm_fit

4 Supplementary figures

4.1 Serial interval distribution

This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.

SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale, w = 0.5)

SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
                                        meanlog = log(4.7),
                                        sdlog = log(2.9), w = 0.5)

SI_dist1 <- data.frame(x = SI_distribution$r(1e5)) 
SI_dist1 <- count(SI_dist1, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 30, 5)) +
    theme_bw()

SI_dist2 <- data.frame(x = SI_distribution2$r(1e5)) 
SI_dist2 <- count(SI_dist2, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
    theme_bw()


ggpubr::ggarrange(SI_dist1,
                  SI_dist2,
                  nrow = 1,
                  labels = "AUTO") 

4.2 Sensitivity analysis - 7 or 21 days moving window

We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.

First with the 7 days window:

## set moving time window (1/2/3 weeks)
w <- 7

# create empty df
r_all_sliding_7days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
plot_R <- r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_7days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_7days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_7 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

Then with the 21 days window:

## set moving time window (1/2/3 weeks)
w <- 21

# create empty df
r_all_sliding_21days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
# plot
plot_R <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_21days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_21days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_21 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

And we combine both outputs into a single plot:


ggpubr::ggarrange(r_R_7,
                  r_R_21,
                  nrow = 2,
                  labels = "AUTO",
                  common.legend = TRUE,
                  legend = "bottom") 

4.3 Correlation between NHS Pathways reports and deaths by NHS region


lag_cor_reg <- data.frame()

for (i in 0:30) {

  summary <-
    all_data %>%
    group_by(nhs_region) %>%
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI for each region
    group_modify(~getboot(.x)) %>%
    mutate(lag = i)
  
  lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}

cor_vs_lag_reg <- 
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
  geom_point() +
  geom_line() +
  facet_wrap(~nhs_region) +
  scale_color_manual(values = pal) +
  scale_fill_manual(values = pal, guide = F) +  
  theme_bw() +
  labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
  theme(legend.position = "bottom") +
  guides(color = guide_legend(override.aes = list(fill = NA)))

cor_vs_lag_reg

5 Export data

We save the tables created during our analysis:


if (!dir.exists("excel_tables")) {
  dir.create("excel_tables")
}


## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")

for (e in tables_to_export) {
  rio::export(get(e),
              file.path("excel_tables",
                        paste0(e, ".xlsx")))
}

## also export result from regression on lagged data 
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))

6 System information

6.1 Outline

The following information documents the system on which the document was compiled.

6.2 System

This provides information on the operating system.

Sys.info()
##                                                                                            sysname 
##                                                                                           "Darwin" 
##                                                                                            release 
##                                                                                           "19.5.0" 
##                                                                                            version 
## "Darwin Kernel Version 19.5.0: Tue May 26 20:41:44 PDT 2020; root:xnu-6153.121.2~2/RELEASE_X86_64" 
##                                                                                           nodename 
##                                                                                   "Mac-1613.local" 
##                                                                                            machine 
##                                                                                           "x86_64" 
##                                                                                              login 
##                                                                                             "root" 
##                                                                                               user 
##                                                                                           "runner" 
##                                                                                     effective_user 
##                                                                                           "runner"

6.3 R environment

This provides information on the version of R used:

R.version
##                _                           
## platform       x86_64-apple-darwin15.6.0   
## arch           x86_64                      
## os             darwin15.6.0                
## system         x86_64, darwin15.6.0        
## status                                     
## major          3                           
## minor          6.3                         
## year           2020                        
## month          02                          
## day            29                          
## svn rev        77875                       
## language       R                           
## version.string R version 3.6.3 (2020-02-29)
## nickname       Holding the Windsock

6.4 R packages

This provides information on the packages used:

sessionInfo()
## R version 3.6.3 (2020-02-29)
## Platform: x86_64-apple-darwin15.6.0 (64-bit)
## Running under: macOS Catalina 10.15.5
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggnewscale_0.4.1     ggpubr_0.3.0         lubridate_1.7.9     
##  [4] chngpt_2020.5-21     cyphr_1.1.0          DT_0.14             
##  [7] kableExtra_1.1.0     janitor_2.0.1        remotes_2.1.1       
## [10] projections_0.5.0    earlyR_0.0.1         epitrix_0.2.2       
## [13] distcrete_1.0.3      incidence_1.7.1      rio_0.5.16          
## [16] reshape2_1.4.4       rvest_0.3.5          xml2_1.3.2          
## [19] linelist_0.0.40.9000 forcats_0.5.0        stringr_1.4.0       
## [22] dplyr_1.0.0          purrr_0.3.4          readr_1.3.1         
## [25] tidyr_1.1.0          tibble_3.0.1         ggplot2_3.3.2       
## [28] tidyverse_1.3.0      here_0.1             reportfactory_0.0.5 
## 
## loaded via a namespace (and not attached):
##  [1] colorspace_1.4-1  selectr_0.4-2     ggsignif_0.6.0    ellipsis_0.3.1   
##  [5] rprojroot_1.3-2   snakecase_0.11.0  fs_1.4.1          rstudioapi_0.11  
##  [9] farver_2.0.3      fansi_0.4.1       splines_3.6.3     knitr_1.29       
## [13] jsonlite_1.6.1    broom_0.5.6       dbplyr_1.4.4      compiler_3.6.3   
## [17] httr_1.4.1        backports_1.1.8   assertthat_0.2.1  Matrix_1.2-18    
## [21] cli_2.0.2         htmltools_0.5.0   prettyunits_1.1.1 tools_3.6.3      
## [25] gtable_0.3.0      glue_1.4.1        Rcpp_1.0.4.6      carData_3.0-4    
## [29] cellranger_1.1.0  vctrs_0.3.1       nlme_3.1-144      matchmaker_0.1.1 
## [33] crosstalk_1.1.0.1 xfun_0.15         ps_1.3.3          openxlsx_4.1.5   
## [37] lifecycle_0.2.0   rstatix_0.6.0     MASS_7.3-51.5     scales_1.1.1     
## [41] hms_0.5.3         sodium_1.1        yaml_2.2.1        curl_4.3         
## [45] gridExtra_2.3     stringi_1.4.6     kyotil_2019.11-22 boot_1.3-24      
## [49] pkgbuild_1.0.8    zip_2.0.4         rlang_0.4.6       pkgconfig_2.0.3  
## [53] evaluate_0.14     lattice_0.20-38   labeling_0.3      htmlwidgets_1.5.1
## [57] cowplot_1.0.0     processx_3.4.2    tidyselect_1.1.0  plyr_1.8.6       
## [61] magrittr_1.5      R6_2.4.1          generics_0.0.2    DBI_1.1.0        
## [65] pillar_1.4.4      haven_2.3.1       foreign_0.8-75    withr_2.2.0      
## [69] mgcv_1.8-31       survival_3.1-8    abind_1.4-5       modelr_0.1.8     
## [73] crayon_1.3.4      car_3.0-8         utf8_1.1.4        rmarkdown_2.3    
## [77] viridis_0.5.1     grid_3.6.3        readxl_1.3.1      data.table_1.12.8
## [81] blob_1.2.1        callr_3.4.3       reprex_0.3.0      digest_0.6.25    
## [85] webshot_0.5.2     munsell_0.5.0     viridisLite_0.3.0